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1. 7 The Chain Rule OBJECTIVES Ø Find the composition of two functions. Ø Differentiate using the Extended Power Rule or the Chain Rule. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
1. 7 The Chain Rule THEOREM 7: The Extended Power Rule Suppose that g(x) is a differentiable function of x. Then, for any real number k, Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3
1. 7 The Chain Rule Example 1: Differentiate Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 4
1. 7 The Chain Rule Example 3: Differentiate Combine Product Rule and Extended Power Rule Simplified: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5
1. 7 The Chain Rule DEFINITION: The composed function and g, is defined as , the composition of f Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 6
1. 7 The Chain Rule Example 5: For Find and Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 7
1. 7 The Chain Rule Example 6: For Find and Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 8
1. 7 The Chain Rule THEOREM 8: The Chain Rule The derivative of the composition Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley is given by 9
1. 7 The Chain Rule Example 7: For find and and Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 10
1. 7 The Chain Rule Example 8: For and find and Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 11
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